178 CHEMICAL ENGINEERING Other Losses.—The rotation loss, or friction loss of the impeller, considered as a flat disk of negligible axial width, as it rotates in the compressed gas, may be obtained from the formula: Rotation loss (horsepower) =0.0737 X (Wl,000)3Z>02dm, where dm is the mean density of the gas (between pi and p2), pounds per cubic foot. At full load this is practically the only loss to be considered, and it is this loss, more frequently than the centrifugal stresses, that determines the pressure rise that may be developed by a single impeller. Short-circuit losses result from the return of part of the ' gas through the impeller to the inlet instead of proceeding to the exit. Part takes place through the axial clearance between the impeller and the casing and decreases as the gas passed by the pump increases. Another part passes up the backs of the vanes, where the static pressure is lowest and the relative velocity highest, and at light loads, passes down the front of the vanes where the static pressure is highest and relative velocity highest. Short-circuit losses are lowest at full load. They are roughly proportional to the impeller outer diameter, the impeller exit width, and the passage height at the discharge-vane inlet. At no load the short-circuit loss is between two and four times the rotation loss, while at full load it is fairly negligible. Centrifugal Compressor Constants and Characteristic Curves—Quantity Constant.—The quantity of gas delivered by a centrifugal compressor is proportional to uaDaba, or, quantity constant = uaDaba. Compressor Constant.—A compressor model can be used with practically the same efficiency for various combinations of quantity and pressure such that K = Q/Vp« where K is the compressor constant, Q and pe are the desired quantity and mean effective pressure, respectively. The compressor constant can be more conveniently written *&K = QN*/pJ*. Two compressors are similar when they have the same compressor constant. In similar compressors all impeller and discharge-vane linear dimensions are in the same ratio as their impeller diameters, while their impeller and discharge vane angles are respectively equal. For the same revolutions per minute the quantities delivered by similar compressors will vary as the cubes of their diameters; the pressures will vary as the squares of their diameters, and the shaft powers will vary as the fifth powers of their diameters. For the same wheel speed the quantity and the power will vary as the square of the diameter, while the pressure will remain constant. Compressor Coefficients.—In order to make the tests on different compressors, or on the same compressor under different circumstances, comparable on a common basis, various coefficients are computed corresponding to the given observations and these coefficients are plotted as characteristic curves. From these curves the pressure, power, and the hydraulic and shaft efficiencies can readily be computed for any quantity of gas and any revolution per minute. The departure of the ratio va/ua from that value for which the compressor was designed determines largely the efficiency of operation. Therefore, va/ua, or its equivalent, Q/ua, is generally used as the abscissa for the characteristic curves of a compressor, and it is designated as the load coefficient, Ce. It is also frequently represented by Q/N. The fluid input coefficient (d) represents the horsepower corresponding to any given observation divided by the cube of the wheel speed. For the case of axial impeller inlet and radial impeller exit, d = 0.00000432Qs/wfl = 0.00000432Ces. Evidently the characteristic curve of d against C€ is a straight line making an angle with Ce whose tangent is 0.00000432s; it may be drawn independently of the actual observations. In general, d = 0.00000216s QV2/ua3, where V2 = 2gH = ua* + wa* - va* - ue* - w* + ve\